SEOUL, Nov 5 (Reuters) - Hyundai Motor Co's and Kia Motors Corp's admission that they overstated the fuel economy of some cars has tainted their reputations, and brand loyalty will be tested in the months ahead after a decade of unbroken success in the United States.

Shares in the South Korean car makers, which had touted superior fuel efficiency in recent marketing campaigns, tumbled some 7 percent on Monday, as investors fretted about the impact on their brands and sales in the all-important North American market. Hyundai alone lost $3.1 billion in market value.

The setback poses a major challenge for Hyundai Chairman Chung Mong-koo who has led a more than doubling of its U.S. sales over the past decade on improved quality and is now focusing on lifting the company's brand image.

High among investor concerns were the cost of compensating customers of the more than one million vehicles affected, as well as the potential for class-action lawsuits in the United States and similar complaints in other countries.

For some analysts, the news was potentially dire.

``This could be a game-changing event in Hyundai's success story,'' said James Yoon, an analyst at BNP Paribas, said in a report. ``We think the potential financial loss is immaterial compared to the potential reputation loss of brand equity.''

But others noted that unlike damaging recall scandals that had affected rivals Toyota Motor Corp and Ford Motor Co , Hyundai and affiliate Kia had been quick to admit to mistakes and announce a compensation plan.

``Those were more serious issues related to safety... Thus the impact on brand-value and U.S. sales may be smaller than those of competitors,'' Citi analyst Ethan Kim said in a note on Monday, adding that investors would have to wait until November and December sales figures to gauge the impact.

Hyundai said in a statement on Monday that its mistakes only affected vehicles sold in North America.

``All Hyundai cars sold in other regions of the world have been properly certified with correct fuel economy ratings by each respective certification agency,'' it said.

The U.S. Environmental Protection Agency (EPA) found the automakers had overstated mileage for 13 Kia and Hyundai models from the 2011 to 2013 model years.

Hyundai and Kia said on Friday the errors stemmed from procedural differences in their mileage tests compared to the EPA tests. The automakers will reimburse current owners for extra fuel costs and issued a full-page newspaper ad on Sunday to apologise.

Mileage labels on most vehicles will now be lowered by one to two miles per gallon (mpg), and the largest adjustment will be six mpg highway for the Kia Soul, the EPA said.

Analysts said the EPA finding could lead to tens of millions of dollars in compensation, adding that new lawsuits could not be ruled out.

The EPA findings were triggered by consumer complaints, including a class-action suit accusing Hyundai of misleading consumers sensitive to high gas prices that its popular 2011 and 2012 Elantra model was more fuel efficient than it actually was.

In its marketing, Hyundai has touted that many of its models get 40 mpg on the highway. In the ``Save the Asterisks'' campaign, Hyundai poked fun at rivals who offered 40 mpg only on specialized, low-volume models.

Now three Hyundai models, the Elantra, Accent and Veloster, as well as the Kia Rio fall short of that mark as will the Hyundai Sonata and Kia Optima hybrids.

Hyundai has, however, come back from serious problems before.

Back in the late 1990s, Hyundai suffered from major quality problems, selling just four models totalling 90,000 units a year in the U.S. market.

But it shifted its focus to improving quality and introduced a 10-year/100,000 mile warranty programme. That programme and incremental steps forward in style and quality, helped revive sales and last year, sales had grown seven-fold to 646,000 cars, giving it its best-ever market share of 5.1 percent.

Offering low priced vehicles and improved quality and style, Hyundai and Kia were also the only car makers that increased U.S. sales during the 2009 global financial crisis. ($1 = 1090.8750 Korean won)